Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems

Table 6

Results of fixed-dimension multimodal benchmark functions.

Benchmark function	Result	Algorithm
		ABC	BA	GGSA	DA	PSOGSA	MFO	LMFO
()	Best	3.000547	3	3	3	3	3	3
	Worst	3.052848	84.00001	30	3.179715	84	3	3.000357
	Mean	3.015989	15.6	7.144215	3.018584	8.4	3	3.000061
	Std	0.015909	25.30177	9.250619	0.049376	20.55036	1.83E − 15	7.19E − 05
()	Best	−1	−1	−1	−1	−1	−1	−1
	Worst	−0.98844	−0.36913	−0.93625	−0.78575	−0.93625	−0.93625	−1
	Mean	−0.99731	−0.71344	−0.949	−0.94932	−0.9915	−0.96175	−1
	Std	0.003196	0.175563	0.025938	0.053641	0.022043	0.031767	0
()	Best	−0.99909	−0.99028	−1	−1	−1	−1	−1
	Worst	−0.98981	−0.54822	−0.99028	−0.92181	−0.99028	−0.99028	−1
	Mean	−0.99095	−0.71504	−0.99286	−0.98153	−0.99093	−0.99061	−1
	Std	0.002023	0.126856	0.004349	0.02047	0.002465	0.001774	0
()	Best	−1	−1	−1	−1	−1	−1	−1
	Worst	−0.99991	−8.1E − 05	−8.1E − 05	−0.95227	−1	−1	−0.99918
	Mean	−0.99999	−0.80002	−0.92221	−0.99656	−1	−1	−0.99973
	Std	2.03E − 05	0.406805	0.257944	0.010494	0	0	0.000229